A096091 -id:A096091 - cp's OEIS frontend

A260461 Numbers k in A096091 such that the nonzero digits of k are not all the same and k/10 is not in the sequence.

105, 108, 150, 180, 405, 450, 501, 504, 510, 540, 801, 810, 1002, 1005, 1008, 1020, 1200, 2001, 2004, 2005, 2010, 2040, 2050, 2100, 2400, 2500, 3006, 3060, 3600, 4002, 4005, 4008, 4020, 4080, 4200, 4800, 5001, 5002, 5004, 5020, 5200, 6003, 6030, 6300, 8001

Offset: 1

Jon E. Schoenfield, Jul 26 2015

A096091 contains infinitely many of each of two types of terms (which are not disjoint): (1) terms whose nonzero digits are all the same, and (2) terms that are 10 times another term in A096091. This sequence lists the terms that remain after removal of all terms that match one or both of those two criteria. See comments in A096091.

Jon E. Schoenfield, Table of n, a(n) for n = 1..1572 (all terms < 10^9)

Cf. A096091, A260462.

A096089 Let f(n) = largest number formed using digits of n, g(n) = smallest number formed using digits of n; then a(n) = floor(f(n)/g(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 2, 2, 3, 3, 4, 4, 4, 10, 1, 1, 1, 1, 2, 2, 2, 2, 3, 10, 2, 1, 1, 1, 1, 1, 1, 2, 2, 10, 2, 1, 1, 1, 1, 1, 1, 1, 1, 10, 3, 2, 1, 1, 1, 1, 1, 1, 1, 10, 3, 2, 1, 1, 1, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 1, 1, 1, 10, 4, 2, 2, 1, 1, 1, 1, 1, 1, 10, 4, 3, 2, 1, 1, 1, 1, 1, 1, 100, 10, 17, 23, 29, 34

Offset: 1

Amarnath Murthy, Jun 22 2004

			a(12324) = floor(43221/12234) = 3.
a(1098) = floor(9810/0189) = 51.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A004186, A004185, A096090, A096091.

A096089 := proc(n)
    floor( A004186(n)/A004185(n)) ;
end proc: # R. J. Mathar, Jul 26 2015

a(n) = d = digits(n); fromdigits(vecsort(d, , 4)) \ fromdigits(vecsort(d))

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jul 19 2004

a(1)..a(9) prepended by David A. Corneth, Jan 21 2019

A096090 Index of the first occurrence of n in A096089, or 0 if n never appears.

Original entry on oeis.org

1, 13, 15, 17, 116, 117, 119, 1119, 0, 10, 506, 304, 203, 508, 305, 509, 102, 1012, 307, 205, 308, 2035, 103, 1033, 2056, 207, 1013, 2067, 104, 1044, 209, 1034, 1024, 105, 1055, 1014, 1045, 106, 1035, 2029, 107, 10225, 1046, 1015, 108, 1036, 109, 1078

Offset: 1

Amarnath Murthy, Jun 22 2004

a(9) = 0. For any number with any 0 digits, A096089(n) >= 10. The only number with n digits and no zeros that can be multiplied by 9 to produce a number with the same number of digits is 111...1, so 9 cannot be achieved. A similar argument shows that a(n) = 0 for any n whose leading digit is 9. Note that a(89) = 1011199; probably every number whose leading digit is not 9 does occur in A096089. - Franklin T. Adams-Watters, Jul 19 2006

			a(7) = 119 as floor[911/119] = floor[7.655462184...] = 7 and 119 is the smallest such number.

R. J. Mathar, List of n, a(n) for n=1..1000 with a(n)=-1 for unknown terms.

Cf. A096089, A096091.

1119 from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jul 19 2004, who remarks that a(9) is not known. The terms after a(9) are 10, 506, 304, 203, 508, 305, 509, 102, 1012, 307, 205, 308, 2035, 103, 1033, 2056, 207, 1013, 2067, 104, 1044, 209, 1034, 1024, 105, 1055, 1014, 1045, 106, 1035, 2029, 107, ...

More terms from Franklin T. Adams-Watters, Jul 19 2006

A260462 Numbers k such that the digits of k are in increasing order and k divides (reverse(k) * 10^m) for some sufficiently-large integer m.

Original entry on oeis.org

12, 15, 16, 18, 24, 25, 36, 45, 48, 125, 128, 144, 168, 225, 256, 288, 1125, 1344, 2688, 12288, 111888

Offset: 1

Jon E. Schoenfield, Jul 26 2015

This sequence consists of the set of distinct numbers that result from taking the terms of A260461, sorting the digits of each term in ascending order, and discarding the leading zeros.
(Equivalently, this sequence consists of the set of distinct numbers that result from taking the terms of A096091 whose nonzero digits are not all the same, sorting the digits of each term in ascending order, and discarding the leading zeros.)
Through a(21) = 111888, the digits 7 and 9 do not appear.
After a(21) = 111888, there are no more terms through 10^27. Presumably, the sequence is full. Is there a proof?

Cf. A096091, A260461.

cp's OEIS Frontend

A260461 Numbers k in A096091 such that the nonzero digits of k are not all the same and k/10 is not in the sequence.

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A096089 Let f(n) = largest number formed using digits of n, g(n) = smallest number formed using digits of n; then a(n) = floor(f(n)/g(n)).

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A096090 Index of the first occurrence of n in A096089, or 0 if n never appears.

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A260462 Numbers k such that the digits of k are in increasing order and k divides (reverse(k) * 10^m) for some sufficiently-large integer m.

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